The Tykes, who have two games in hand on their rivals, jumped out of the bottom three after last week's home win over Crystal Palace and followed up by taking a point at Derby on Saturday.
Davey said: "We're only three points above the relegation zone and we're by no means out of danger yet.
"We've had a good performance and got a point, but now we've got a two-week break and we need to get everybody refreshed and ready for Nottingham Forest.
"Hopefully when they come to our stadium three points behind us and us having two games in hand we can capitalise on that and beat them.
"It's nice to continue when you're in this form, but a few of the players picked up knocks. We get rest and recuperation now for the Nottingham Forest game."